Forgotten old results break my motivation

In my experience, any material that you do not regularly brush up on, you forget. Sometimes partially, sometimes completely. You don't learn things once, then know them forever. You learn things once, then you remember the stuff that you need again and again. So don't get discouraged when you have to brush up on old material in order to understand new material, think of it as a chance to brush up on material in order to keep that material within your grasp. At some point, when you have had to brush up on certain material enough times, it will stick. This is part of a natural process where you forget material that you don't need, whereas the stuff you need is set in stone.

Always remember that the stuff you need is probably different from the stuff some other mathematician needs. So the process is unique to you, and in the long run defines the type of mathematician you become.


This also has to do with how you used to study. I always forced myself to be able to reproduce everything from scratch. Deriving everything from first principles with all books closed on a blank piece of paper is a bit more time consuming, but this yields superior results.

To this date I can reproduce most of what I learned decades ago without needing to look up anything. The only reason I do look up things is because that saves me time. When I have to teach and I want to refresh my skills, I'll first reproduce the entire theory on a black piece of paper just like I did when I was a student. Only then will I look at the books. I'll then know what I should pay attention to.

What helped me here was the fact that I started studying from advanced math and physics topics from university books when I was still in high school. I therefore had plenty of time on my hands, not under any pressure to submit homework of to be prepared for exams. And then when I went to unversity I was so far ahead that I could just go on with that routine.